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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 38640.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bl1 | 38640ca4 | \([0, -1, 0, -13460821080, 601116546812400]\) | \(65853432878493908038433301506521/38511703125000000\) | \(157743936000000000000\) | \([4]\) | \(30965760\) | \(4.1009\) | |
| 38640.bl2 | 38640ca2 | \([0, -1, 0, -841306200, 9392541895152]\) | \(16077778198622525072705635801/388799208512064000000\) | \(1592521558065414144000000\) | \([2, 2]\) | \(15482880\) | \(3.7543\) | |
| 38640.bl3 | 38640ca3 | \([0, -1, 0, -809946200, 10125011143152]\) | \(-14346048055032350809895395801/2509530875136386550792000\) | \(-10279038464558639312044032000\) | \([2]\) | \(30965760\) | \(4.1009\) | |
| 38640.bl4 | 38640ca1 | \([0, -1, 0, -54546520, 135212796400]\) | \(4381924769947287308715481/608122186185572352000\) | \(2490868474616104353792000\) | \([2]\) | \(7741440\) | \(3.4077\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38640.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.bl do not have complex multiplication.Modular form 38640.2.a.bl
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
